I guess I would call Woody Guthrie's Jesus Christ a non-humorous parody of this song, depending on how one defines "parody." "Jesus Christ" is in Rise Up Singing, but not "Jesse."

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As the Ballad Index entry says above, Carl Sandburg's American Songbag has two versions of Jesse I. This one is "heavily folk-processed." Sandburg says this is the "negro version of the Jesse James ballad, as heard by Charles Rockwood in work gangs of the south.

I Went down to the Depot

I went down to the depot, not many nights ago,
And there I done something I never done before.
I got down on my knees
And delivered up the keys
To Frank and his brother Jesse James.
Po' Jesse James, po' Jesse James,
I'll never see my Jesse any more;
'Twas a dirty little coward
He shot Mister Howard
An' laid Jesse James in his grave.

Jesse James was a man and he had a robber band:
And he flagged down the east bound train.
Robert Ford watched his eye,
And he shot him on the sly,
And they laid Jesse James in his grave.
Po' Jesse James, po' Jesse James
I'll never see my Jesse any more.
'Twas a dirty little coward
That shot Mister Howard
And laid Jesse James in his grave.

Jesse James' little wife was a moaner all her life
When they laid Jesse James in his grave.
She earned her daily bread
By her needle and her thread
When they laid Jesse James in his grave.
Po' Jesse James, po' Jesse James,
I'll never see my Jesse any more.
Robert Ford's pistol ball
Brought him tumbling from the wall
And laid Jesse James in his grave.